I took a look at your op.gg.
You peaked at Plat 5 100 LP during the end of the season and the pre-season of Season 7, the time were people don't play seriously, so it doesn't really count. I'd put you in the Gold 1 elo bracket, which means you are not that much better than the competition you are facing to be stomping them and have something like a 70% win rate. Now, on to analyzing the other things.
You play way too many champions. You don't get to train a lot of a single champion to know them well, their limits, their tricks etc, and that can play a big role, especially since the champions you play a lot are Renekton, Kassadin and Galio. You need to focus on a few champions.
Your cs/min is horrible. It doesn't matter how well you do in lane, how many times you managed to kill your enemy, or how much pressure you were able to take and not feed. All it matters is how much you can outpace your enemies so that you are stronger regardless of if your team feeds them or not. The way you do that is to take advantage of any resource that's on the map to get gold and xp leads. You don't do that. You don't cs well, especially on champions who are supposedly easy to cs on, like Ziggs and Renekton. On Kassadin, it's even more horrible. You need to understand that League is a racing game; the player who's the fastest to reach a certain point will most likely win, and guess what, you're falling behind. You can't carry with your pace, because others are outpacing you, which brings me to my next point.
Don't play Galio, don't play Kassadin. Even Renekton is risky. If you're not willing to play jungle (and if you're not good at it, I suggest you stay away), then play something that is:
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safe in lane, doesn't need to take risks, so that it can cs well and level up safely
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have the tools to impact the early game, especially after level 6.
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be a safe champion overall in all stages of the game, while being able to deal damage and/or offer utility.
Let's analyze.
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Having safety in lane is important. It means you don't really fall back no matter what happens. Even if you get ganked, you have the tools to repel it, and can then keep on csing. This means that you get cs and xp, which, as covered above, are extremely important to not fall behind in the race, while also not feeding the enemy. Guess which champion doesn't do that; Kassasin. You will naturally fall behind with Kassadin, and that's not good.
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Impacting the early game is the most important thing. If you can help your team not feed, then you will probably win. Guess who doesn't do that; Kassadin. Or Renekton with Ignite, as you like to play him. You need to be able to make plays and assist your team. Galio isn't good either, because it requires a teammate to be in the correct spot so you can ulti.
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Safe champion in all stages, damage/utility. This means that they need to have as many of the following traits as possible: mobility spell (dash, blink or even MS boost), range, damage, CC. Kassadin doesn't have that. He has blinks and damage, but doesn't have CC or range, which means that you need to have a team to play around your own strengths, and you won't find that in soloQ.
All the 3 points above lead to certain champions you need to play in order to have good chances to win. Taliyah is a good example. Safe laning with her pushing power and CC to repel ganks. Good damage to win 1v1s in lane, good range to safely cs and not fall behind. Then, she can roam even as a level 3, because of her passive, making her roaming so much more potent at level 6 with her R, so she can help her team quite a lot. She's also very safe (has the MS boost) because of her long range, her zoning field and her knock back, while offering damage and CC.
Other champions that fit that description are Annie, Ahri, Lucian, most ADCs (well, not in this patch anymore) and things like Irelia, Vladimir etc. All of the have quite a safe laning phase, with a lot of impact in the mid game and great late game.